Contextualization
Exponential equations are fundamental mathematical tools that assist in the representation and resolution of situations involving exponential growth or decay in various areas of knowledge. It is an equation in which the unknown appears in the exponent. Common examples include the expansion of a population of bacteria, the radioactive decay of a material, population growth, and compound financial yields.
In our daily lives, exponential equations are present in contexts of constant growth and decay, such as the decay rate of a medication in the body, the population growth of a city, and even the depreciation of a vehicle over time. The understanding of exponential equations allows the interpretation of the behavior of these phenomena and the prediction of future behaviors, therefore being essential for decision-making based on mathematical models.
Atividade Prática: Desvendando os Mistérios das Funções Exponenciais
Activity Title: "Exponential: In Practice"
Project Objective:
Our goal with this project is to understand in a practical and playful way the exponential equations, involving their resolution, the interpretation of the variation of the quantities involved, and the application of these concepts in contexts of constant growth and decay.
Project Description:
Students will be divided into groups (3 to 5 students) and must choose a real phenomenon that can be modeled by an exponential function. Each group will conduct an experiment, record data collection, and finally analyze the collected data using exponential equations.
Based on the observations and analyses carried out, the groups must write a complete report on the experience, which will be shared with the class. Students will also make an oral presentation of their results.
Necessary Materials:
- Materials for the experiment execution (varies depending on the chosen experiment)
- Computer with internet access.
- Spreadsheet software (such as Microsoft Excel or Google Sheets).
- Materials for the presentation (may vary depending on the format chosen by each group).
Detailed Step-by-Step:
Step 1 - Group Formation and Choice of Phenomenon to be Analyzed: The groups should already have been formed. Each group must choose a phenomenon to be studied that can be represented by an exponential function.
Step 2 - Planning and Execution of the Experiment: The groups must plan and carry out an experiment that allows data collection. Data collection should then be carried out in a way that allows subsequent analysis using exponential functions.
Step 3 - Data Analysis: Using spreadsheet software, students will analyze the collected data. Equations representing the studied situation should be created to extrapolate the data for future scenarios.
Step 4 - Report Elaboration: Students must elaborate a project report. The report should include an introduction (with contextualization of the theme and relevance of the study), detailed description of the experiment execution, description of data analysis processes, and discussion of results.
Step 5 - Preparation of the Presentation: In parallel with the report elaboration, groups must prepare a presentation of the results obtained to be presented to the class.
Step 6 - Presentation of Results: Each group will make an oral presentation of their results to the class.
Project Deliverables:
- Written Report: This document is the central piece of the delivery and should detail all aspects of the project, from the choice of the phenomenon to be analyzed, the preparation and execution of the experiment, the data collection and analysis, to the conclusion of the work. The report should be written clearly and concisely.
- Presentation: Each group must make an oral presentation to the class, explaining the results of their experiment and the conclusions drawn from the data.
The project deliveries are directly linked to the suggested activities above. Carrying out the experiment and analyzing the collected data are fundamental for the elaboration of the report and the presentation, which are the final project deliveries. Therefore, it is expected that students acquire technical and socio-emotional skills, such as time management, communication, problem-solving, creative thinking, and proactivity.
The report writing should follow the suggested structure: Introduction, Development (with detailed description of the experiment, data analysis, and discussion of results), Conclusions (with a return to the main points of the introduction, explaining the learnings obtained and the conclusions drawn about the project), and Bibliography used.
